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BUS708 Statistics And Data Analysis For Australian Taxation Office

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Questions:

1. Give a brief introduction about the assignment, including your research question.
 
Include a short summary of a related article with a proper citation.
 
b. Dataset 1: Give a short description about this dataset. Is this primary or secondary data? What types of variable(s) is involved? Display the first 5 cases of your dataset.
 
c. Dataset 2: Explain how you collect the data and discuss its limitation (e.g. whether your sample is biased). Is this primary or secondary data? What type of variable(s) is/are involved? You don’t need to display your data in this section.

Answer:

Introduction:

The data set is collected from the Australian Taxation Office (ATO). The data set would help to find the gender gap of salary between men and women. The reasons of gender gap generate the discrimination of hiring in the job. The salary as well as occupation according to the different gender varies significantly. The data set summarises the analysis regarding job profile of women and men in different industries. Their salary or wage and donation or gift amounts. We considered the data file as “College data”. The data set includes totally 1000 samples.

The research question is:

“Is there any difference of the average salary amount between male and females in data set2?” (Dietl et al. 2012).

The data set 1 is a secondary data. The data is not collected by researcher himself. ATO has delivered the data to the researcher for analysis.

The data set have a total of 4 variables. These are Gender (Sex), Occ_code (Salary/wage occupation code), sw_amt (Salary/wage amount) and Gift_amt (Gifts or dination deductions). Here, salary/wage amount and Gift_amt are numerical variable as these have numerical values. Gender is a nominal (Categorical) variable having two levels “Male” and “Female” (Dietl et al. 2012). Occupation code of salary/wage is also a nominal variable which is transformed in numerical variables such as Sales workers implies 6.

Not only that, in the second part, the data of only gender type and salary/wage is tabulated with the help of survey. This second data set is named as “College” data. The data is collected by random sampling method. The simple data collection method randomly had received the responses from 100 males and females of the college. Out of them, only 63 people, responded about their amount of salary.

The data set is collected with the help of ground survey with a simple questionnaire of two questions: 1) “What is your gender?” 2) “What is your salary amount?”.

The data is primary in nature to the researcher. The data set involves one numerical (salary/wage) and one categorical (Gender) variable.

Descriptive Statistics

The graph shows that the number of female workers is higher for two occupations- “Clerical and Administrative workers” and “Professionals”. On the other hand, the number of male workers is higher for two occupations- “Technicians and Trade Workers” and “Professionals”.

Females earn lesser salary than males as an average (57830.74 > 31768.51). The salaries of males are more scattered than the salaries of females in terms of standard deviation (67008.17>32603.49). The minimum wages for both the genders are 0. The maximum wage/ salary of any male is greater than maximum wage/salary of any female (839840>308183) (Wigginton and Abecasis 2005). The proportions of “Manager” (1) males and females are 0.610 and 0.390 respectively.
  • The proportions of “Professional” (2) males and females are 0.513 and 0.487 respectively.
  • The proportions of “Technicians and Trade Worker” males and females are 0.843 and 0.157.
  • The proportions of “Machinery operators and driver” males and females are 0.929 and 0.071 respectively.
  • The proportions of males and females in all 4 types of occupations are 0.667 and 0.333.

Hypotheses:

Null hypothesis (H0): The proportion of males among all the machinery operators and drivers is 0.8.

Alternative hypothesis (HA): The proportion of males among all the machinery operators and drivers is greater than 0.8.

Out of 42 machinery operators and drivers 39 are found to be males.

Level of significance: 0.05.

Calculated proportion: The observed proportion is 0.928571.

Hypothetical proportion: 0.8

Z-calculated: 2.083095.

Z-critical: 1.959964.

Decision making: As, 2.083095 > 1.959964, therefore, Z-calculated > Z-critical. It helps to reject the null hypothesis with 95% probability (Palocsay, Markham and Markham 2010). The alternative hypothesis is accepted.

Interpretation: The proportion of males among all the machinery operators and drivers is greater than 80%.

 

Hypotheses:

Null hypothesis (H0): The average salary/wage amounts of males and females are equal to each other.

Alternative hypothesis (HA): The average salary/wage amounts of males is greater than the average salary/wage amounts of females.

Table 6: Tables of two-sample t-test assuming equal and unequal variances

Out of 1000 samples, 461 are females and 539 are males. The average salary/wage of females is 31768.51 and the average salary/wage of males is 57830.74.

Level of significance: 0.05.

Calculated t-statistics: (-7.991298903) for unequal variances.

Two tailed p-values: (4.61956E-15) for unequal variances.

Decision making: As, the two-tailed p-value is less than 0.05, therefore, it helps to reject the null hypothesis with 95% probability. The alternative hypothesis is accepted (Norušis 2006).

Interpretation: It could be interpreted with 95% probability that the average salary/wage amounts of males is greater than the average salary/wage amounts of females.

Hypotheses:

Null hypothesis (H0): The average salary/wage amounts of males is equal with the average salary of males for data set2.

Alternative hypothesis (HA): The average salary/wage amounts of males are greater the average salary of females for data set2.

Data set2 has 63 samples. The average salary/wage of males of data set2 is 51166.60 and the average salary/wage of females of data set2 is 38987.33.

Level of significance: 0.05.

Calculated t-statistics: (-1.3162676) for unequal variances.

Two tailed p-values: (0.197734245) for unequal variances.

Decision making: As, the two-tailed p-value is greater than 0.05, therefore, it helps to accept the null hypothesis with 95% probability. The alternative hypothesis is rejected.

Interpretation: It could be interpreted with 95% probability that the average salary/wage amounts of males is equal to the average salary/wage amounts of females of data set2.

The average salary of males is equal to the average salary/wage amount females in data set 2 with 95% probability. Therefore, no difference is present for average salaries of both the gender in this data set.

Discussion and Conclusion

The previous sections help to conclude some facts that-

Females generally prefer to do the jobs of clerical and administrative as well as professional jobs. Males prefer to do the job of technicians and trade workers as well as professional jobs. Professional jobs are preferred by both the genders. The salary or wage is greater for males than females. It is also significantly proven in the below section. However, this claim is not proved in data analysis of data set 2. In this analysis, no significant difference of average salaries of males and females is obtained. Conversely, the gift amount provided to the females is greater than males. Out of 9 selected occupations, the salary is higher as per the middle most values in the professions of “Manager”, “Professionals”, “Technicians and Trades Workers” and “Machinery operators and drivers”. The machinery operator and drivers are dominated by the males as the percentages of males are greater than 80%. Therefore, occupation also has a greater role to determine gender proportion as salary amount has (Chung, 2009).

The future research that of this topic is that-

The number of samples of data set2 could be drawn more. The causes relating the amount of salary of the males, females or both could be detected. Data on those specified topics should be collected from the target population (Burns and Burns 2008). Not only that, those parameters should be included in the data sets. More information could be extracted from the analysed dataset if the information regarding years of experience, educational level, hours of working and designation of work are added in the data set (Black 2009).

 

References:

Bates, D., Maechler, M., Bolker, B. and Walker, S., 2014. lme4: Linear mixed-effects models using Eigen and S4. R package version, 1(7), pp.1-23.

Black, K., 2009. Business statistics: Contemporary decision making. John Wiley & Sons.

Chung, S., Domino, M.E., Stearns, S.C. and Popkin, B.M., 2009. Retirement and physical activity: analyses by occupation and wealth. American journal of preventive medicine, 36(5), pp.422-428.

Dietl, H.M., Franck, E., Lang, M. and Rathke, A., 2012. Salary cap regulation in professional team sports. Contemporary economic policy, 30(3), pp.307-319.

Jelen, B. and Alexander, M., 2010. Pivot Table Data Crunching: Microsoft Excel 2010. Pearson Education.

Jelen, B., 2010. Charts and Graphs: Microsoft Excel 2010. Que Publishing.

Norušis, M.J., 2006. SPSS 14.0 guide to data analysis. Upper Saddle River, NJ: Prentice Hall.

Palocsay, S.W., Markham, I.S. and Markham, S.E., 2010. Utilizing and teaching data tools in Excel for exploratory analysis. Journal of Business Research, 63(2), pp.191-206.

Wigginton, J.E. and Abecasis, G.R., 2005. PEDSTATS: descriptive statistics, graphics and quality assessment for gene mapping data. Bioinformatics, 21(16), pp.3445-3447.

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